Kelly criterion
Definition
The Kelly criterion is a formula for the optimal share of the deposit to put into a single trade, derived from your share of winning trades and the payout percent. It gives the share at which capital grows fastest over a long distance; in practice traders take a fraction of it — a quarter or a half — because full Kelly produces drawdowns too deep to sit through.
What the formula computes
The Kelly criterion answers a question money management usually settles by convention: what share of the deposit goes into a trade. Instead of the "1–2%" standard it derives the share from two of your own numbers — the share of winning trades and the payout percent — and finds the one at which capital grows fastest over a long distance.
Staking more is harmful: growth slows down while drawdowns deepen. Staking less is safe but slower. Full Kelly is the boundary past which a larger amount starts working against you rather than for you.
For binary options the formula is short: (win rate × (1 + payout) − 1) / payout, with the payout taken as a fraction of one. The denominator is that same asymmetry of the payout: profit equals the payout while a loss always equals the whole amount.
What it comes out to in practice
An 85% payout, whose breakeven threshold sits at 54.05%:
| Your win rate | Full Kelly | Quarter Kelly |
|---|---|---|
| 54% | — | — |
| 55% | 2.06% | 0.51% |
| 58% | 8.59% | 2.15% |
| 60% | 12.94% | 3.24% |
| 65% | 23.82% | 5.96% |
The first row is the most useful thing in this table. At a 54% win rate and an 85% payout the formula returns a negative share, that is, it declines the trade: 54% is below the 54.05% threshold, and there is nothing to trade on. No share saves you here — this is not a money-management problem.
The second useful row is the last one. At a 65% win rate full Kelly suggests staking almost a quarter of the deposit on a single trade. Formally that is the optimum for growth speed; in fact it is the road to a drawdown after which few people keep trading by the rules. Hence the quarter: 5.96% instead of 23.82%.
Putting it to work
You can compute your own share with the Kelly calculator: it shows full and fractional Kelly, the expected growth of capital and the point where growth falls to zero from an inflated share.
The one condition is honest inputs. The win rate has to come from your actual statistics rather than from a feeling: the difference between 58% and 60% changes the share by half again. If you have no statistics yet, the 1–2% position size standard is safer than any calculation built on an imagined win rate.
How it differs from a fixed percent
A fixed percent sets the share by convention: 1–2% of the deposit regardless of how good the setup is. Kelly derives the share from your numbers, so a strong strategy gets a larger one and a weak one gets zero.
The practical difference is what you trust. A fixed percent does not require knowing your win rate — it simply keeps you from going broke. Kelly requires statistics and punishes self-deception: a win rate inflated by a couple of points produces an inflated share, and that hurts the account more than falling short on growth speed does. So the usual arrangement is to live on a fixed percent and use Kelly as a check — am I staking too much.
Frequently asked questions
How is the Kelly share computed for binary options?
The share equals (win rate × (1 + payout) − 1) / payout, with the payout taken as a fraction of one. At a 60% win rate and an 85% payout that gives (0.60 × 1.85 − 1) / 0.85 = 12.9% of the deposit. The formula only works above the breakeven threshold — below it the result is negative.
Why is full Kelly not used?
Because it optimises the speed of growth, not your peace of mind: at a 12.9% share per trade the drawdowns reach tens of percent, and sitting through them is close to impossible. Meanwhile fractional Kelly gives up growth far more gently than it gives up risk: half the share keeps about 75% of the maximum speed and a quarter about 44%, while the drawdown shrinks several times over. That is why a fraction is what gets used.
What if the formula returns a negative share?
Do not trade that setup. A negative share means your win rate sits below the breakeven threshold for this payout: any amount on such a trade loses money on average. The formula is not "suggesting something smaller" — it is saying there is nothing to stake.